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Why Lawrenceville Plasma Physics Results are Not Even Wrong; a Detailed Analysis.

June 20, 2012

I recently responded to a claim from Lawrenceville Plasma Physics that they were close to a commercial fusion reactor.  I was annoyed that such claims were being made and even more concerned that such claims were not receiving a strong criticism from the scientific community.  I read the paper published in the journal – Physics of Plasma by Lerner and his colleagues.  The journal is a reputable peered reviewed publication. It was clear to me that the paper was not significant. Dense plasma focus devices are well understood and have been modelled in detail. The results quoted by Lerner did not show that the focus device which he has developed was significantly better than other devices and there was no evidence that a commercial fusion device was any closer.

I was dubious if the paper had achieved its claim of proving that fusion was the result of confined ions rather than beam ions hitting the pinch plasma (non-thermal fusion).  This would indeed be a new result and would contravene the well-known and well accepted current theories that exist. The key point is that Lerner’s device still follows the scaling laws of other devices even if he proposes a different interpretation of results.  The different interpretation does not increase the yield from his device nor does it bring him any closer to commercial fusion.

My conclusion was that Lerner had not built a novel device and had not proved or indeed disproved anything. He had replicated a standard focus device and the paper was not even wrong.  I was contacted by Lerner and asked to explain my position. So I have prepared a short paper to refute Lerner’s claims and justify my conclusion and explain to those who might be interested the reality behind Lerner’s claims. I also want to make it clear that I have no vested interest other than seeking clarity and the truth and I respect Lerner’s right to do experiments and make claims based on his results. 

To clarify the original claim I quote from the LPP web site

On March 23rd, 2012, we published in the journal Physics of Plasmas a report of the confinement of plasma with ion energy equivalent to 1.8 billion degrees C for a period of tens of nanoseconds using a dense plasma focus device. This achieved two out of three conditions—temperature and confinement time—needed not just for fusion energy, but for fusion energy using advanced, aneutronic fuels that have long been considered out of reach. We did all this with an innovative device costing less than one million dollars. If we are able to achieve the third condition, density, we could be on track to commercializing fusion within five years.

For background I will give a quick review of the concept of a dense plasma focus device. The key is that a high voltage is applied between an anode and a cathode. The electrodes have radii A and B, with A>B.  A gap exists between A and B and an insulator shields part of the anode from the cathode.  A plasma forms in the gap and is pushed along the anode by magnetic fields generated by the high discharge current. When the plasma reaches the end of the anode a pinch column forms where the anode had been and this has a very high density and temperatures. This focus is sometimes called a plasmoid.  The ion energy is such that in a deuterium gas, a significant amount of neutrons are produced from fusion reactions.

It is generally accepted that the main mechanism producing the neutrons is a beam of fast deuteron ions interacting with the hot dense plasma of the focus pinch column. The origin of the fast ion beam is a diode action in a thin layer close to the anode with deviations from neutrality generating the necessary high voltages. This mechanism has been modelled in detail based on a expression for fusion yield given below;

Yb-t      =     calibration constant x ni Ipinch2 zp2(ln(b/rp))σ/Vmax0.5

where Ipinch is the current at the start of the slow compression phase, rp and zp are the pinch radius and pinch length at the end of the slow compression phase, Vmax is the maximum value attained by the inductively induced voltage, σ is the D-D fusion cross section (n branch)corresponding to the beam ion energy and ni is the pinch ion density. The D-D cross section σ is obtained by using beam energy equal to 3 times Vmax, to conform to experimental observations. 

Data is available  for the neutron yield Yn from a wide range of machines and can be used to calibrate the model and also to establish a clear empirical scaling law.  It has been shown that the log of the neutron flux is linear with the log of the Ipeak.

Table 1 data from plasma focus devices

A comparison of data from a wide number of plasma focus devices worldwide

 The pinch current is higher for smaller diameters of anode, so a correction factor is required to convert Ipeak to Ipinch. In the case of LPP, I used 0.58 which is the factor measured for the NX2 device which is similar in anode dimensions to the LPP device.  

Figure 1, Data from a wide range of plasma focus devices world wide showing the standard scaling law.

Figure 1, shows a log-log plot of Neutron flux versus Ipinch, LPP best data point in red.

I have included the best result reported by Lerner, which is 1.1Ma and 1.5 1011   neutrons.  It is clear from the paper that other shots at 1.1Ma had a lower yield. Figure 2, in Lerner’s paper shows three points at the highest ion energy ( highest Ipeak) and the spread is at least a factor of 3.  So Lerner’s result fit exactly with all other Plasma Focus devices. What is different is that he drives a large current into a small radius anode, but the device scales just as expected. No new physics here I am afraid.  I have to commend his team on making a solid job of measuring everything and proving that they have a standard plasma focus device, they could have got the calibration of some of the instrumentation wrong and then we might have had less clarity.

I would be interested to hear comments from you on whether you consider this an issue in science today and the role of the web in publishing “Facts” that might mislead.

For more information on the modeling of plasma focus devices and as a reference source for the data used here please see,

Neutron Scaling Laws from Numerical Experiments, S Lee & S H Saw, Journal of Fusion Energy,  2008.

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  1. P Liddi permalink

    Great blog, Mike. The net is full of new ideas and claims but people never hear first hand from experts. Best of luck to LLP and anyone pursuing fusion power, but lets keep it real.

  2. Alvaro permalink

    But is focused fusion a device fundamentally capped in its possibilities?
    Could you ilustrate a bit on the history of it and why you think it cannot succeed?

  3. Wooaa neddy. According to the legend of the graph above (and accompanying text) this whole piece is an “annoyed” rebuttal based as it is on LPP results seeming to fit somewhat neatly on a plot of neutron yields from typical DPF experimentation into deuterium+tritium fusion.

    While on first glance that all seems sensible, if in fact the LPP red dot for neutron flux was generated by a side reaction of LPP’s aneutronic fusion of p+B11 (and NOT a principally neutron-yielding deuterium-tritium reaction) then this article runs the risk of missing the point to an alarming degree.

  4. Gavriel State permalink

    Does the CCHEN nanofocus device fit this linear scaling? Looking at and they are showing ~10E3 neutron production for a device that has a peak current of 15 kA. With a similar calibration factor to the other devices in your list, that seems to put their neutron production well above your line, at least according to my crude on-screen estimates.

    Could there not be a possibility of similar higher output from LPPs device, given that they too are pushing larger currents through a smaller electrode geometry?

  5. Dennis T permalink

    Never mind my question. I just learned that Coulomb interactions are electrostatic interactions, not electromagnetic.

  6. The empirical factors you refer to may be due impurities in the fusion fuel such as vaporised electrode. LPP has confirmed copper ions are present. The empirical factors may be common to all prior DPFs but probably not to LPP when they install their tungsten electrodes, which should resist vaporisation much better than their current copper electrodes.

  7. As Dr. Mike Hopkins is not posting his criticism in peer-reviewed journals, reply coming from the Indiegogo Crowdfunding QA:
    >On the Web, links lead to an analysis by Mike Hopkins calling your results “not even wrong.” What is your reply?–3?show_todos=true

    Dr. Hopkins’ analysis misses the whole point of our July 2012 paper, which was about our demonstrating record-breaking temperatures in our confined plasma. Hopkins complained that we had not demonstrated record-breaking fusion yields. But yields depend not only on temperature but on densities as well and we were not claiming any superior density or yield. The paper was about the record temperatures. It was demonstrating that this temperature—sufficient to ignite hydrogen-boron fuel, was indeed confined in a small plasmoid that made our paper the most-read one of 2012 in Physics of Plasma, the leading journal in our field. Evidently a lot of our colleagues got the point, even if Dr. Hopkins missed it. As to densities, we expect to greatly improve them and achieve record fusion yields as well in our next series of experiments.”

  8. Andrea Di Vita permalink

    Admittedly, LPP paper focussed on temperature, not on DD neutron yield. However, Dr. Hopkins s right when invoking well-known scaling laws in assessing LPP performances. The interested reader may find further discusson in A. Di Vita, Eur. Phys. J. D (2013) 67: 191. In my opinion, Lerner’s arguments neglect the adverse role of Joule dissipation, and lead therefore to overoptimistic predictons. Few strategies in order to overcome this problem are also discussed in the paper. . ,

  9. It sounds like Dr. Hopkins is simply pointing out that the LPP method follows long-established scaling laws for plasmas. This implies that getting usable amounts of power require scaling up to the sizes of “conventional” fusion plasma machines. We likely will still need an ITER-scale machine costing $billions, even if dense plasma focus fusion works.
    In the bigger picture, it appears that we have forgotten the knowledge hard-won by the professional nuclear physicists and engineers of the 1950’s and 1960’s. This a case where six years in the lab saves six hours in the library!

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